I have never had a Dell laptop overheat, but I do see where the dust could be a problem. I will give it a try. But perhaps all the "vent" holes on the back of the HP would allow dust to accumulate faster.
First unplug it and shut it down, blow air backwards though the out vents to loosen up the crude, then blow through the inlet to blow it out or it will get lodged in the inlet screen. Repeat as necessary until you don't see stuff blowing out. But don't over do it or you could damage the fan blade, but that has never happened to me.
Canned air does not have enough pressure, but a air compressor would likely hurt it if blown too hard, which is why I suggested the canned air.